文档介绍：理论力学 Theoretical Mechanics
运动学第八章刚体平面运动
力学教研室
Planar Kinematics of Rigid Bodies PART A Concepts and Velocities
Planar Kinematics of Rigid Bodies
PART A Concepts
What is planar motion
The distance of each points on the rigid body to a fixed plane is a constant value, this kind of motion is said to be planar motion
Planar Kinematics of Rigid Bodies
Motion Equation
Separation mon planar motion
Suppose the body AB moves mon planar motion, analyze the motion of point B
Motion Equation of A:
We chose A as the base point (基点)of the rigid body, setup coordinates system O’x’y’ fixed on A
Absolute Motion : Motion of B Relative Motion: Rotation about fixed axis on point A Convected Motion: Translation of O’x’y’
Planar Kinematics of Rigid Bodies
Velocity of the point on rigid body
Method of Relative velocity
1 Method of Relative Velocity
Chose MP: point B DF(translation) fixed on A
Where w is the angular velocity of the body AB
Planar Kinematics of Rigid Bodies
Velocity of the point on rigid body
Theorem of projection of velocities
2 Theorem of Projection of Velocities
At an instant time, velocities of any two points have the same projection to the line between these two points (Deduction is omitted)
Planar Kinematics of Rigid Bodies
Velocity of the point on rigid body
Sample problem1
3 Sample problem 1
GO!
OA=r, AB=b, O1B=d
w is a constant value.
Compute wAB and w1
Planar Kinematics of Rigid Bodies
Velocity of the point on rigid body
Sample problem1
3 Sample problem 1
[solution]
Chose A as the base point
Draw the diagram of velocities
Planar Kinematics of Rigid Bodies
Velocity of the point on rigid body
In Class Exercise
4 In Class Exercise
GO!
w is a constant value.
Compute wAB and vB
Suppose j=60o, OA=r and AB=l
Hint : use the theorem of projection of velocities.
Planar Kinematics of Rigid Bodies
Velocity of the point on rigid body
Concept of Instant Center
5 Concept of Instant Center
The Instant Center (瞬心)for velocities o